Table 1.

Comparison of types of predictors for which parameter values may differ over individuals in multiple groups (MG), multiple-indicator multiple-cause (MIMIC), MIMIC-interaction, and moderated nonlinear factor analysis (MNFLA) models.

Parameters	Model
	MG*	MIMIC	MIMIC-Interaction	MNLFA
α	Categorical	Categorical and Continuous	Categorical and Continuous	Categorical and Continuous
Ψ	Categorical	-	-	Categorical and Continuous
ν	Categorical	Categorical and Continuous	Categorical and Continuous	Categorical and Continuous
Λ	Categorical	-	Categorical and Continuous	Categorical and Continuous
Σ	Categorical	-	-	Categorical and Continuous

Note: α = factor means; Ψ = variance-covariance matrix of latent factors; ν = item intercepts; Λ = factor loadings; Σ = variance-covariance matrix of item residuals.

^*MG model also allows for the possibility of distinct factor structures in each group, permitting tests of configural invariance.